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Preheat oven to 350.
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Butter 2 baking sheets.
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In a medium bowl, cream together butter and sugar until smooth.
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Beat in eggs one at a time, then stir in the milk, vanilla and, lemon extract.
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Combine cake flour and all-purpose flour, baking powder, and salt; gradually blend into the creamed mixture.
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Drop tablespoons of the dough at least 2 inches apart on prepared sheet.
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Bake until edges begin to brown; checking in 10 minutes.
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Cool completely.
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To make icing: Place confectioners sugar in a large bowl.
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Mix in boiling water one tablespoon at a time until mixture is thick and spreadable.
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Transfer half of the frosting to the top of a double boiler set over simmering water.
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Stir in chocolate.
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Warm mixture, stirring frequently, until chocolate melts.
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Remove from heat.
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With a brush, coat half the cookie with chocolate frosting and the other half with white frosting.
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Set on wax paper until frosting hardens.